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+"""Unit tests for the :mod:`networkx.algorithms.minors.contraction` module."""
+
+import pytest
+
+import networkx as nx
+from networkx.utils import arbitrary_element, edges_equal, nodes_equal
+
+
+def test_quotient_graph_complete_multipartite():
+ """Tests that the quotient graph of the complete *n*-partite graph
+ under the "same neighbors" node relation is the complete graph on *n*
+ nodes.
+
+ """
+ G = nx.complete_multipartite_graph(2, 3, 4)
+ # Two nodes are equivalent if they are not adjacent but have the same
+ # neighbor set.
+
+ def same_neighbors(u, v):
+ return u not in G[v] and v not in G[u] and G[u] == G[v]
+
+ expected = nx.complete_graph(3)
+ actual = nx.quotient_graph(G, same_neighbors)
+ # It won't take too long to run a graph isomorphism algorithm on such
+ # small graphs.
+ assert nx.is_isomorphic(expected, actual)
+
+
+def test_quotient_graph_complete_bipartite():
+ """Tests that the quotient graph of the complete bipartite graph under
+ the "same neighbors" node relation is `K_2`.
+
+ """
+ G = nx.complete_bipartite_graph(2, 3)
+ # Two nodes are equivalent if they are not adjacent but have the same
+ # neighbor set.
+
+ def same_neighbors(u, v):
+ return u not in G[v] and v not in G[u] and G[u] == G[v]
+
+ expected = nx.complete_graph(2)
+ actual = nx.quotient_graph(G, same_neighbors)
+ # It won't take too long to run a graph isomorphism algorithm on such
+ # small graphs.
+ assert nx.is_isomorphic(expected, actual)
+
+
+def test_quotient_graph_edge_relation():
+ """Tests for specifying an alternate edge relation for the quotient
+ graph.
+
+ """
+ G = nx.path_graph(5)
+
+ def identity(u, v):
+ return u == v
+
+ def same_parity(b, c):
+ return arbitrary_element(b) % 2 == arbitrary_element(c) % 2
+
+ actual = nx.quotient_graph(G, identity, same_parity)
+ expected = nx.Graph()
+ expected.add_edges_from([(0, 2), (0, 4), (2, 4)])
+ expected.add_edge(1, 3)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_condensation_as_quotient():
+ """This tests that the condensation of a graph can be viewed as the
+ quotient graph under the "in the same connected component" equivalence
+ relation.
+
+ """
+ # This example graph comes from the file `test_strongly_connected.py`.
+ G = nx.DiGraph()
+ G.add_edges_from(
+ [
+ (1, 2),
+ (2, 3),
+ (2, 11),
+ (2, 12),
+ (3, 4),
+ (4, 3),
+ (4, 5),
+ (5, 6),
+ (6, 5),
+ (6, 7),
+ (7, 8),
+ (7, 9),
+ (7, 10),
+ (8, 9),
+ (9, 7),
+ (10, 6),
+ (11, 2),
+ (11, 4),
+ (11, 6),
+ (12, 6),
+ (12, 11),
+ ]
+ )
+ scc = list(nx.strongly_connected_components(G))
+ C = nx.condensation(G, scc)
+ component_of = C.graph["mapping"]
+ # Two nodes are equivalent if they are in the same connected component.
+
+ def same_component(u, v):
+ return component_of[u] == component_of[v]
+
+ Q = nx.quotient_graph(G, same_component)
+ assert nx.is_isomorphic(C, Q)
+
+
+def test_path():
+ G = nx.path_graph(6)
+ partition = [{0, 1}, {2, 3}, {4, 5}]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1
+
+
+def test_path__partition_provided_as_dict_of_lists():
+ G = nx.path_graph(6)
+ partition = {0: [0, 1], 2: [2, 3], 4: [4, 5]}
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1
+
+
+def test_path__partition_provided_as_dict_of_tuples():
+ G = nx.path_graph(6)
+ partition = {0: (0, 1), 2: (2, 3), 4: (4, 5)}
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1
+
+
+def test_path__partition_provided_as_dict_of_sets():
+ G = nx.path_graph(6)
+ partition = {0: {0, 1}, 2: {2, 3}, 4: {4, 5}}
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1
+
+
+def test_multigraph_path():
+ G = nx.MultiGraph(nx.path_graph(6))
+ partition = [{0, 1}, {2, 3}, {4, 5}]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1
+
+
+def test_directed_path():
+ G = nx.DiGraph()
+ nx.add_path(G, range(6))
+ partition = [{0, 1}, {2, 3}, {4, 5}]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 0.5
+
+
+def test_directed_multigraph_path():
+ G = nx.MultiDiGraph()
+ nx.add_path(G, range(6))
+ partition = [{0, 1}, {2, 3}, {4, 5}]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 0.5
+
+
+def test_overlapping_blocks():
+ with pytest.raises(nx.NetworkXException):
+ G = nx.path_graph(6)
+ partition = [{0, 1, 2}, {2, 3}, {4, 5}]
+ nx.quotient_graph(G, partition)
+
+
+def test_weighted_path():
+ G = nx.path_graph(6)
+ for i in range(5):
+ G[i][i + 1]["w"] = i + 1
+ partition = [{0, 1}, {2, 3}, {4, 5}]
+ M = nx.quotient_graph(G, partition, weight="w", relabel=True)
+ assert nodes_equal(M, [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ assert M[0][1]["weight"] == 2
+ assert M[1][2]["weight"] == 4
+ for n in M:
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1
+
+
+def test_barbell():
+ G = nx.barbell_graph(3, 0)
+ partition = [{0, 1, 2}, {3, 4, 5}]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1])
+ assert edges_equal(M.edges(), [(0, 1)])
+ for n in M:
+ assert M.nodes[n]["nedges"] == 3
+ assert M.nodes[n]["nnodes"] == 3
+ assert M.nodes[n]["density"] == 1
+
+
+def test_barbell_plus():
+ G = nx.barbell_graph(3, 0)
+ # Add an extra edge joining the bells.
+ G.add_edge(0, 5)
+ partition = [{0, 1, 2}, {3, 4, 5}]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M, [0, 1])
+ assert edges_equal(M.edges(), [(0, 1)])
+ assert M[0][1]["weight"] == 2
+ for n in M:
+ assert M.nodes[n]["nedges"] == 3
+ assert M.nodes[n]["nnodes"] == 3
+ assert M.nodes[n]["density"] == 1
+
+
+def test_blockmodel():
+ G = nx.path_graph(6)
+ partition = [[0, 1], [2, 3], [4, 5]]
+ M = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(M.nodes(), [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M.nodes():
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1.0
+
+
+def test_multigraph_blockmodel():
+ G = nx.MultiGraph(nx.path_graph(6))
+ partition = [[0, 1], [2, 3], [4, 5]]
+ M = nx.quotient_graph(G, partition, create_using=nx.MultiGraph(), relabel=True)
+ assert nodes_equal(M.nodes(), [0, 1, 2])
+ assert edges_equal(M.edges(), [(0, 1), (1, 2)])
+ for n in M.nodes():
+ assert M.nodes[n]["nedges"] == 1
+ assert M.nodes[n]["nnodes"] == 2
+ assert M.nodes[n]["density"] == 1.0
+
+
+def test_quotient_graph_incomplete_partition():
+ G = nx.path_graph(6)
+ partition = []
+ H = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(H.nodes(), [])
+ assert edges_equal(H.edges(), [])
+
+ partition = [[0, 1], [2, 3], [5]]
+ H = nx.quotient_graph(G, partition, relabel=True)
+ assert nodes_equal(H.nodes(), [0, 1, 2])
+ assert edges_equal(H.edges(), [(0, 1)])
+
+
+def test_undirected_node_contraction():
+ """Tests for node contraction in an undirected graph."""
+ G = nx.cycle_graph(4)
+ actual = nx.contracted_nodes(G, 0, 1)
+ expected = nx.cycle_graph(3)
+ expected.add_edge(0, 0)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_directed_node_contraction():
+ """Tests for node contraction in a directed graph."""
+ G = nx.DiGraph(nx.cycle_graph(4))
+ actual = nx.contracted_nodes(G, 0, 1)
+ expected = nx.DiGraph(nx.cycle_graph(3))
+ expected.add_edge(0, 0)
+ expected.add_edge(0, 0)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_undirected_node_contraction_no_copy():
+ """Tests for node contraction in an undirected graph
+ by making changes in place."""
+ G = nx.cycle_graph(4)
+ actual = nx.contracted_nodes(G, 0, 1, copy=False)
+ expected = nx.cycle_graph(3)
+ expected.add_edge(0, 0)
+ assert nx.is_isomorphic(actual, G)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_directed_node_contraction_no_copy():
+ """Tests for node contraction in a directed graph
+ by making changes in place."""
+ G = nx.DiGraph(nx.cycle_graph(4))
+ actual = nx.contracted_nodes(G, 0, 1, copy=False)
+ expected = nx.DiGraph(nx.cycle_graph(3))
+ expected.add_edge(0, 0)
+ expected.add_edge(0, 0)
+ assert nx.is_isomorphic(actual, G)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_create_multigraph():
+ """Tests that using a MultiGraph creates multiple edges."""
+ G = nx.path_graph(3, create_using=nx.MultiGraph())
+ G.add_edge(0, 1)
+ G.add_edge(0, 0)
+ G.add_edge(0, 2)
+ actual = nx.contracted_nodes(G, 0, 2)
+ expected = nx.MultiGraph()
+ expected.add_edge(0, 1)
+ expected.add_edge(0, 1)
+ expected.add_edge(0, 1)
+ expected.add_edge(0, 0)
+ expected.add_edge(0, 0)
+ assert edges_equal(actual.edges, expected.edges)
+
+
+def test_multigraph_keys():
+ """Tests that multiedge keys are reset in new graph."""
+ G = nx.path_graph(3, create_using=nx.MultiGraph())
+ G.add_edge(0, 1, 5)
+ G.add_edge(0, 0, 0)
+ G.add_edge(0, 2, 5)
+ actual = nx.contracted_nodes(G, 0, 2)
+ expected = nx.MultiGraph()
+ expected.add_edge(0, 1, 0)
+ expected.add_edge(0, 1, 5)
+ expected.add_edge(0, 1, 2) # keyed as 2 b/c 2 edges already in G
+ expected.add_edge(0, 0, 0)
+ expected.add_edge(0, 0, 1) # this comes from (0, 2, 5)
+ assert edges_equal(actual.edges, expected.edges)
+
+
+def test_node_attributes():
+ """Tests that node contraction preserves node attributes."""
+ G = nx.cycle_graph(4)
+ # Add some data to the two nodes being contracted.
+ G.nodes[0]["foo"] = "bar"
+ G.nodes[1]["baz"] = "xyzzy"
+ actual = nx.contracted_nodes(G, 0, 1)
+ # We expect that contracting the nodes 0 and 1 in C_4 yields K_3, but
+ # with nodes labeled 0, 2, and 3, and with a -loop on 0.
+ expected = nx.complete_graph(3)
+ expected = nx.relabel_nodes(expected, {1: 2, 2: 3})
+ expected.add_edge(0, 0)
+ cdict = {1: {"baz": "xyzzy"}}
+ expected.nodes[0].update({"foo": "bar", "contraction": cdict})
+ assert nx.is_isomorphic(actual, expected)
+ assert actual.nodes == expected.nodes
+
+
+def test_edge_attributes():
+ """Tests that node contraction preserves edge attributes."""
+ # Shape: src1 --> dest <-- src2
+ G = nx.DiGraph([("src1", "dest"), ("src2", "dest")])
+ G["src1"]["dest"]["value"] = "src1-->dest"
+ G["src2"]["dest"]["value"] = "src2-->dest"
+ H = nx.MultiDiGraph(G)
+
+ G = nx.contracted_nodes(G, "src1", "src2") # New Shape: src1 --> dest
+ assert G.edges[("src1", "dest")]["value"] == "src1-->dest"
+ assert (
+ G.edges[("src1", "dest")]["contraction"][("src2", "dest")]["value"]
+ == "src2-->dest"
+ )
+
+ H = nx.contracted_nodes(H, "src1", "src2") # New Shape: src1 -(x2)-> dest
+ assert len(H.edges(("src1", "dest"))) == 2
+
+
+def test_without_self_loops():
+ """Tests for node contraction without preserving -loops."""
+ G = nx.cycle_graph(4)
+ actual = nx.contracted_nodes(G, 0, 1, self_loops=False)
+ expected = nx.complete_graph(3)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_contract_loop_graph():
+ """Tests for node contraction when nodes have loops."""
+ G = nx.cycle_graph(4)
+ G.add_edge(0, 0)
+ actual = nx.contracted_nodes(G, 0, 1)
+ expected = nx.complete_graph([0, 2, 3])
+ expected.add_edge(0, 0)
+ expected.add_edge(0, 0)
+ assert edges_equal(actual.edges, expected.edges)
+ actual = nx.contracted_nodes(G, 1, 0)
+ expected = nx.complete_graph([1, 2, 3])
+ expected.add_edge(1, 1)
+ expected.add_edge(1, 1)
+ assert edges_equal(actual.edges, expected.edges)
+
+
+def test_undirected_edge_contraction():
+ """Tests for edge contraction in an undirected graph."""
+ G = nx.cycle_graph(4)
+ actual = nx.contracted_edge(G, (0, 1))
+ expected = nx.complete_graph(3)
+ expected.add_edge(0, 0)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_multigraph_edge_contraction():
+ """Tests for edge contraction in a multigraph"""
+ G = nx.cycle_graph(4)
+ actual = nx.contracted_edge(G, (0, 1, 0))
+ expected = nx.complete_graph(3)
+ expected.add_edge(0, 0)
+ assert nx.is_isomorphic(actual, expected)
+
+
+def test_nonexistent_edge():
+ """Tests that attempting to contract a nonexistent edge raises an
+ exception.
+
+ """
+ with pytest.raises(ValueError):
+ G = nx.cycle_graph(4)
+ nx.contracted_edge(G, (0, 2))
generated by cgit v1.2.3 (git 2.47.1) at 2025-07-27 13:36:01 +0000